## X(85) (ISOTOMIC CONJUGATE OF X(9))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           b2c2/(b + c - a) : c2a2/(c + a - b) : a2b2/(a + b - c)
= tan(A/2) csc2A : tan(B/2) csc2B : tan(C/2) csc2C

Barycentrics    bc/(b + c - a) : ca/(c + a - b) : ab/(a + b - c)

X(85) lies on these lines:
1,664    2,241    7,8    12,120    29,34    56,870    57,274    76,226    92,331    109,767    150,355    264,309

X(85) = isogonal conjugate of X(41)
X(85) = isotomic conjugate of X(9)
X(85) = complement of X(3177)
X(85) = anticomplement of X(1212)
X(85) = X(274)-Ceva conjugate of X(348)
X(85) = cevapoint of X(I) and X(J) for these (I,J): (1,169), (2,7), (57,77), (92,342)
X(85) = X(I)-cross conjugate of X(J) for these (I,J): (2,75), (57,273), (92,309), (142,2), (226,7)

X(85) = X(I)-beth conjugate of X(J) for these (I,J):
(76,76), (85,279), (99,1), (274,85), (668,85), (789,85), (799,85), (811,85)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.